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Skip to 0 minutes and 4 seconds Rudolf Clausius recognised that heat flows spontaneously from a high temperature body to a low temperature body. And then he realised is the reverse is not true, which leads to the statement of the second law. Heat does not pass from body at low temperature to a high temperature without an accompanying change elsewhere. In other words, we can move heat in the wrong direction, but has to be paid for, usually with work.

Skip to 0 minutes and 33 seconds So this statement of the second law, heat is not pass from a body at a low temperature to one at a high temperature without an accompanying change elsewhere, could be summarised in a little equation here that Clausius developed, where this sigma here means integration around the cycle, and we have the change in heat divided by the temperature which that change occurs. And that has to be less than or equal to zero.

Skip to 1 minute and 4 seconds So a quantity whose cycle is an integral of zero depends only on the state, and not on the process path that we take. And that means that that quantity must be a property. Clausius recognised this, and realised that he defined a new property that he called entropy. And so we can rewrite this. Here’s my same expression here, and now I put an equal sign. Equal to 0 and equal to Δs, where s stands for entropy. And this is true for a reversible process.

Skip to 1 minute and 43 seconds All real processes, however, are irreversible. And we can normally identify one of three main forms of irreversibility. These are factors that cause a process not to be reversible. And the first one is heat transfer across a finite temperature difference. And the second one is the unrestrained expansion of a gas. The sort of thing that happens when you take a balloon [BANG] and you pop it. And then the third type is friction. And we have supply work to overcome friction. And that’s converted to heat and is dissipated. So if I rub this along the table, I’ll eventually generate some heat in the sheet here and on the table, and that will be dissipated. But it’s not only between solids.

Skip to 2 minutes and 30 seconds It’s also internal to fluids. So if I was to stir this for long enough, eventually I generate heat here as the fluid molecules rub past one another. We can also get it with fluid - solid interaction at the boundary of the fluid in the glass.

Skip to 2 minutes and 48 seconds This leads to the definition of entropy in a more generic statement of the second and that is that the entropy of the universe increases in the course of a spontaneous change. And this context, the universe means the system that we’ve defined, and the surroundings. Everything else. So there’s no prohibition on entropy decreasing inside our system, or in the surroundings, providing there’s a compensating increase elsewhere.


Rudolf Clausius recognised heat only moves spontaneously from hot to cold and that work must be supplied to move energy in the opposite direction. Watch Eann explain how this led to the concept of entropy and that all real processes are irreversible, including popping balloons.

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This video is from the free online course:

Energy: Thermodynamics in Everyday Life

University of Liverpool